“These astronomical calculations [ramadan calendars /timetables] are different to one another. At times the difference between one [timetable] to another is six minutes [difference]. And this isn’t something small and especially for the Adhaan for Fajr and the Adhaan for Maghrib since both are connected to fasting though it is necessary that all timings [for prayer] be observed correctly. So if two timetables are different to each other and both have been produced by those who are qualified and knowledgeable for the timings of the prayer, then we should give precedence to the latest timing of the two, [this is] for all the prayers since the orgin is that the time hasn’t yet entered bearing in mind that both calculations have been produced from people of such expertises… ”

“… Therefore, the muadhin should wait approximately five minutes after the prescribed time [on the timetable sheet] which is found with the people nowadays. The reason being according to the correct astronomical calculations that the timetable is five minutes ahead throughout the year especially for Salat Al-Fajr and what is compulsory is to be cautious because if a person were to proceed the time [for prayer] by an amount of merely saying takbir al-ihram, then his prayer wouldn’t be valid. Thus, it is compulsory to be cautious and alhamdulilah it won’t be of any harm if you were to delay for five minutes then make adhaan.”

[Sharh Bulooghul Maraam, Chapter al-Mawaaqeet]

A Side Note: The fact the skies are still quite dark doesn’t necessitate that these timetables are erroneous since the Prophet sallahu alayhi wa salam used to pray Fajr at its earliest time while it was still dark as come in some narrations.